The Big 50 Revision Guidelines for S1

Transcription

1 The Big 50 Revision Guidelines for S1 If you can understand all of these you ll do very well 1. Know what is meant by a statistical model and the Modelling cycle of continuous refinement 2. Understand how inferences from a suitably representative sample can be used to study the wider population 3. Name at least three sampling techniques and describe the relative advantages and disadvantages of each in terms of practicality, economy and reliability 4. Know how to categorise data types according to labels such as discrete, continuous, qualitative and quantitative and be able to give real-life examples of each 5. Understand the distinction between Upper/Lower Class Boundaries and Upper/Lower Class Limits, and why the Upper Class Boundary is used in cumulative frequency graphs 6. Understand that graphical representation can result in loss of data, especially through oversimplification 7. Know how to construct a cumulative frequency step polygon 8. Know how to construct a single or double sided Stem and Leaf diagram 9. Know a variety of techniques for the display of data and understand that according to context some are more effective than others 10. Understand the necessary calculations of frequency density and area required for the construction and interpretation of variable-width histograms 11. Understand the distinction between Measures of Central Tendency (Location) and Measures of Dispersion (Spread) and give examples of each 12. Know how to interpret the Mode, Median and Mean of a set of data, and how to estimate these from a grouped frequency chart, including interpolation as necessary 1

2 13. Understand what is meant by the Coding of data, and the implications on the calculation of the mean of the original data set 14. Appreciate the conventions used for the determination of Upper and Lower Quartiles from a small set of discrete data (n < 50) when n/4 is or is not an integer 15. Understand and use the formula to find the r th of s quantiles within a given class, given the lower class boundary b, the total frequency n, the cumulative frequency f up to b, the class frequency c and the class width w 16. Appreciate the assumptions made when interpolating or extrapolating data 17. Know how to find the quartiles, both from a cumulative frequency graph and from a grouped frequency chart, and to use them to describe the skewness of a data set 18. Know how to calculate a measure of skewness using the mean, median and s.d. 19. Know how to calculate the variance and standard deviation of a set of data, and how to do this efficiently on a scientific calculator 20. Understand the notation used to describe overlapping and disjoint sets (Venn Diagram notation) and the graphical interpretation of Union, Intersection and Complement 21. Understand the simplifications made for probability work at KS3 and GCSE, and how these are extended into more general contexts at KS5 22. Know the meaning of Dependent, Independent, Mutually Exclusive and Conditional in the context of probability 23. Understand how to apply the formula to calculate the probability of one event given the probability of another 24. Understand and use the notation P(A), P(A'), P(A B), P(A B) and P(A B) 25. Given P(C), P(S C) and P(S C ), know how to calculate (for example) P(S C ), P(S) and P(C S), and be able to give both a graphical illustration and a real-life context for these calculations 2

3 26. Understand why P(A B) P(B A) 0 for mutually exclusive events A and B. 27. Understand why P(A C) P(A) and P(C A) P(C) implies that events A and C are independent 28. Understand and use the Addition and Multiplication Rules for probability 29. Know how to use probability trees and Venn Diagrams to solve probability problems 30. Know how to use the factorial function n! to calculate number of arrangements, and to use the n formula r or n C r to deal with repeated items 31. Understand and use a Probability Distribution Function P(X x) for a discrete random variable and appreciate why for all such PDFs, P(X x) Appreciate the distinction between unbiased (n 1) and biased (n) estimators for the calculation of the population variance from the sample data 33. Understand and use the Expectation of a random variable, and of a function of a random variable, where in general E(g(x)) g(x)p(x x) 34. Appreciate that E(X 2 ) E(X) 2 and be able to explain the difference 35. Know how to write the Mean and Variance of a random variable X in terms of E(X), E(X 2 ) and E 2 (X) [E(X)] Know how to calculate the Expectation and Variance of a linear function of a random variable: E(aX b) and Var(aX b) 37. Understand the concept of Correlation between the two variables in a bivariate data set as a measure of the quality of a best fit line 38. Understand the concept of Linear Regression as a means of fitting a straight line through a set of data points, especially by the Method of Least Squares 3

4 39. Understand the distinction between the regression line y on x and the regression line x on y, and know when each is appropriate 40. Know how to calculate S xx, S xy and S yy given n, x, y, xy, x 2 and y Know how to calculate and interpret (Pearson s) Product Moment Correlation Coefficient PMCC, especially with the assistance of a scientific calculator 42. Know how to calculate the equation of a regression line of A on B, especially with the assistance of a scientific calculator 43. Understand why the Regression Line must go through the Mean Point x, y 44. Understand the concept of a Normal Distribution and the Standard Normal Distribution, and the standardising process from X Z 45. Understand and use tables or scientific calculator to determine approximate areas under the Normal curve between any two points 46. Know the relationship between areas under the Normal curve and associated probability calculations for a Normally-distributed continuous random variable 47. Know the approximate percentages of a Normal distribution contained within ±1, ±2 and ±3 standard deviations of the mean 48. Know how to use the symmetry of the Normal Distribution to calculate related probabilities 49. Know how to interpret phrases such as at least, between, no more than etc. in the context of probability questions 50. Know how to interpret tabulated or calculated values in the context of the original problem. 4

5 This really is it the big one. If you can answer YES to all 50 of these questions then you can feel confident about any Stats Exam they might throw at you. Here goes:! Do you know the shape of the two skewed distributions?! Can you use a random number table to generate a set of random numbers?! Do you know how to calculate Standard Deviation and Variance?! Do you know how to estimate population size using the Petersen Capture/ Recapture method?! Can you say when it is best to use dual or stacked bar charts?! Can you sketch examples of two non-linear relationships?! Can you give three examples of both primary and secondary data?! Can you give three examples of both qualitative and quantitative data?! Do you know what is meant by the Population of a statistical study?! Would you know what to do with time series data?! Can you calculate and use the equation of a line of best fit?! Do you know the difference between univariate and bivariate data?! Can you draw the diagrams for under-simplification and over-simplification?! Can you give three examples of both discrete and continuous data?! Can you explain when and how to use a weighted mean?! Can you operate with Warning and Action Limits for Quality Control?! Can you explain the purpose of a pilot survey?! Can you interpret graphs and charts and comment on misleading representations?! Can you name three measures of central tendency?! Can you draw stem and leaf diagrams either one sided or back-to-back?! Can you use interpolation to estimate the median of grouped data?! Do you know how to calculate outliers and show them on a box and whisker plot?! Can you use Sigma Notation for the mean of grouped data?! Can you use interval notation correctly without gaps or overlaps?! Do you know how to calculate and plot moving averages and trend lines?

6 ! Can you explain when and how to use the geometrical mean?! Can you draw and use probability trees?! Can you name three measures of dispersion?! Can you explain Frequency Density in Histograms?! Can you explain why standardised scores are the best way to compare exam results in two different subjects?! Can you explain how to do stratified sampling?! Can you give three examples of different scales used for data?! Do you know how to reduce bias in sampling?! Can you say why interpolation is more accurate than extrapolation on a scattergraph?! Can you explain how quartiles, deciles and percentiles fit on a cumulative frequency graph?! Can you calculate probabilities associated with discrete uniform distributions?! Can you calculate and interpret Spearman's Rank Correlation Coefficient?! Can you name ten different statistical charts and diagrams?! Do you know the central percentages of the Normal Distribution associated with ± 1, 2 or 3 SDs?! Can you describe four sampling techniques with their pros and cons?! Do you know the difference between independent (explanatory) and dependent (response) variables?! Can you calculate probabilities associated with the Binomial Distribution?! Can you say when it is a good idea to use comparative frequency polygons?! Can you use simple examples of conditional probability?! Can you say why a sample should be representative?! Do you know why a hypothesis can never be proved?! Do you know how to use Venn Diagrams?! Can you work with comparative pie charts?! Do you know the difference between Hypothesis and Sub-Hypothesis?! Can you use chain base and index numbers to show changes in data?

GCSE Statistics Revision notes Collecting data Sample This is when data is collected from part of the population. There are different methods for sampling Random sampling, Stratified sampling, Systematic

GCSE HIGHER Statistics Key Facts Collecting Data When writing questions for questionnaires, always ensure that: 1. the question is worded so that it will allow the recipient to give you the information

Summary of Formulas and Concepts Descriptive Statistics (Ch. 1-4) Definitions Population: The complete set of numerical information on a particular quantity in which an investigator is interested. We assume

INTERNATIONAL BACCALAUREATE (IB) MATH STANDARD LEVEL, YEARS 1 AND 2 Grades 11, 12 Unit of Credit: 1 Year for Year 1 and 1 Year for Year 2 Pre-requisite: Algebra 2 for Year 1 IB Math Standard Level Year

Mathematics Probability and Statistics Curriculum Guide Revised 2010 This page is intentionally left blank. Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction

A Correlation of to the South Carolina Data Analysis and Probability Standards INTRODUCTION This document demonstrates how Stats in Your World 2012 meets the indicators of the South Carolina Academic Standards

BNG 202 Biomechanics Lab Descriptive statistics and probability distributions I Overview The overall goal of this short course in statistics is to provide an introduction to descriptive and inferential

Probability and Statistics Vocabulary List (Definitions for Middle School Teachers) B Bar graph a diagram representing the frequency distribution for nominal or discrete data. It consists of a sequence

LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 12O ELEMENTARY STATISTICS I 3 Lecture Hours, 1 Lab Hour, 3 Credits Pre-Requisite:

A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes together with the number of data values from the set that

Topic 1 Algebra The aim of this topic is to introduce students to some basic algebraic concepts and applications. Check Topic 1 Book Arithmetic sequences and series; Sum of finite arithmetic series; Geometric

OCR Statistics Module Revision Sheet The S exam is hour 30 minutes long. You are allowed a graphics calculator. Before you go into the exam make sureyou are fully aware of the contents of theformula booklet

Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2015 Examinations Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in

Central Tendency Central Tendency n A single summary score that best describes the central location of an entire distribution of scores. n Measures of Central Tendency: n Mean n The sum of all scores divided

2. Describing Data We consider 1. Graphical methods 2. Numerical methods 1 / 56 General Use of Graphical and Numerical Methods Graphical methods can be used to visually and qualitatively present data and

Minitab Guide This packet contains: A Friendly Guide to Minitab An introduction to Minitab; including basic Minitab functions, how to create sets of data, and how to create and edit graphs of different

Statistics GCSE Higher Revision Sheet This document attempts to sum up the contents of the Higher Tier Statistics GCSE. There is one exam, two hours long. A calculator is allowed. It is worth 75% of the

REVISED GCSE Scheme of Work Mathematics Higher Unit T3 For First Teaching September 2010 For First Examination Summer 2011 Version 1: 28 April 10 Version 1: 28 April 10 Unit T3 Unit T3 This is a working

Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.

Seminar paper Statistics The seminar paper must contain: - the title page - the characterization of the data (origin, reason why you have chosen this analysis,...) - the list of the data (in the table)

REVISION SHEET STATISTICS 1 (MEI) THE BINOMIAL DISTRIBUTION & PROBABILITY The main ideas in this chapter are Probabilities based on selecting or arranging objects Probabilities based on the binomial distribution

WHAT IT IS Return to Table of ontents Descriptive statistics include the numbers, tables, charts, and graphs used to describe, organize, summarize, and present raw data. Descriptive statistics are most

Chapter 3: Data Description Numerical Methods Learning Objectives Upon successful completion of Chapter 3, you will be able to: Summarize data using measures of central tendency, such as the mean, median,

Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics (or inductive statistics),

MATH BOOK OF PROBLEMS SERIES New from Pearson Custom Publishing! The Math Book of Problems Series is a database of math problems for the following courses: Pre-algebra Algebra Pre-calculus Calculus Statistics

Page 1 of 16 Chapter 2: Exploring Data with Graphs and Numerical Summaries Graphical Measures- Graphs are used to describe the shape of a data set. Section 1: Types of Variables In general, variable can

NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York DEPARTMENT: Mathematics COURSE: MAT 1272/ MA 272 TITLE: DESCRIPTION: TEXT: Statistics An introduction to statistical methods and statistical

Quantitative Methods for Finance Module 1: The Time Value of Money 1 Learning how to interpret interest rates as required rates of return, discount rates, or opportunity costs. 2 Learning how to explain

DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,

13.2 Measures of Central Tendency Measures of Central Tendency For a given set of numbers, it may be desirable to have a single number to serve as a kind of representative value around which all the numbers

Week 1 Exploratory Data Analysis Practicalities This course ST903 has students from both the MSc in Financial Mathematics and the MSc in Statistics. Two lectures and one seminar/tutorial per week. Exam

Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 2009-2010 Week 1 Week 2 14.0 Students organize and describe distributions of data by using a number of different

Terms and Definitions Absolute Value the magnitude of a number, or the distance from 0 on a real number line Additive Property of Area the process of finding an the area of a shape by totaling the areas

LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 119 STATISTICS AND ELEMENTARY ALGEBRA 5 Lecture Hours, 2 Lab Hours, 3 Credits Pre-

Statistics for Engineers 4-1 4. Introduction to Statistics Descriptive Statistics Types of data A variate or random variable is a quantity or attribute whose value may vary from one unit of investigation

Pie Charts and Bar Charts: III. GRAPHICAL METHODS Pie charts and bar charts are used for depicting frequencies or relative frequencies. We compare examples of each using the same data. Sources: AT&T (1961)

MODE The mode of the sample is the value of the variable having the greatest frequency. Example: Obtain the mode for Data Set 1 77 For a grouped frequency distribution, the modal class is the class having

At the end of the lesson, you should be able to: Chapter 2: Systems of Linear Equations and Matrices: 2.1: Solutions of Linear Systems by the Echelon Method Define linear systems, unique solution, inconsistent,

YEAR 8 SCHEME OF WORK - SECURE Autumn Term 1 Number Spring Term 1 Real-life graphs Summer Term 1 Calculating with fractions Area and volume Decimals and ratio Straight-line graphs Half Term: Assessment

Exploratory Data Analysis Psychology 3256 1 Introduction If you are going to find out anything about a data set you must first understand the data Basically getting a feel for you numbers Easier to find

STATISTICS FOR PSYCH MATH REVIEW GUIDE ORDER OF OPERATIONS Although remembering the order of operations as BEDMAS may seem simple, it is definitely worth reviewing in a new context such as statistics formulae.

UNIVERSITY OF PUNE Syllabi for First Year Bachelor of Science (Computer Science) With Effect From Academic Year 2008-2009 Subject : Statistics (1) Statistics Paper I - Statistical Methods - I (Total Marks

Descriptive Statistics Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion Statistics as a Tool for LIS Research Importance of statistics in research

Chapter 15 Multiple Choice Questions (The answers are provided after the last question.) 1. What is the median of the following set of scores? 18, 6, 12, 10, 14? a. 10 b. 14 c. 18 d. 12 2. Approximately

The Analysis of Research Data The design of any project will determine what sort of statistical tests you should perform on your data and how successful the data analysis will be. For example if you decide

Numerical Summarization of Data OPRE 6301 Motivation... In the previous session, we used graphical techniques to describe data. For example: While this histogram provides useful insight, other interesting

Lecture 1 1 Lecture I Definition 1. Statistics is the science of collecting, organizing, summarizing and analyzing the information in order to draw conclusions. It is a process consisting of 3 parts. Lecture

Summarizing and Displaying Categorical Data Categorical data can be summarized in a frequency distribution which counts the number of cases, or frequency, that fall into each category, or a relative frequency